orthogonal bases
Complete
Summary
Relative coordinates to an orthogonal basis
Relative coordinates to an orthonormal basis
Orthogonal matrices
Concept
Orthogonality and linear independence
- not every orthogonal set is linearly independent -> can contain the 0 vector
- every orthonormal set is linearly independent
Orthogonal/orthonormal basis
- if the orthogonal set spans a subspace
- similar properties to the standard basis
Orthogonal matrices preserve norm
orthogonal matrices do not scale
Core idea of orthogonal matrices
Product of orthogonal matrices is orthogonal
Determinants of orthogonal matrices
Application
Relative coordinates
orthogonal matrices preserve angle and distance between relative coordinates
Rotation matrix